TS EAMCET · Maths · Binomial Theorem
Assertion (A) : \(1+\frac{2.1}{3.2}+\frac{2.5}{3.6} \frac{1}{4}+\frac{2.5 .8}{3.6 .9} \frac{1}{8}+\ldots \infty=\sqrt[3]{4}\) Reason (R): \(|x| \lt 1\), \((1-x)^{-n}=1+n x+\frac{n(n+1)}{1.2} x^2+\frac{n(n+1)(n+2)}{1.2 .3} x^3+\ldots\) The correct answer is
- A (A) and (R) are correct, (R) is the correct explanation of (A)
- B (A) and (R) are correct, but (R) is not the correct explanation of (A)
- C (A) is correct but (R) is not correct
- D (A) is not correct but (R) is correct
Answer & Solution
Correct Answer
(A) (A) and (R) are correct, (R) is the correct explanation of (A)
Step-by-step Solution
Detailed explanation
\((1-x)^{-n}=1+n x+\frac{n(n+1)}{1.2} x^2+\frac{n(n+1)(n+2)}{1.23} x^3+\ldots\) Put \(x=\frac{1}{2}, n=\frac{2}{3}\)…
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